Optimizing Epochal Evolutionary Search: Population-Size Dependent Theory

Technological change at the firm level has commonly been modeled as random sampling from a fixed distribution o f possibilities. Such models, however, typically ignore empirically important aspects of the firm's search process, notably the observation that the present state of the firm guides future innovation. In this paper we explicitly treat this apsect of the firm's search for technological improvements by introducing a "technology landscape" into an otherwise standard dynamic programming setting where the optimal strategy is to assign a reservation price to each possible technology. Search is modeled as movement, constrained by the cost of innovation, over the technology landscape. Simulations are presented on a stylized technology landscape while analytic results are derived using landscapes that are similar to Markov random fields. We find that early in the search for technological improvements, if the inital position is poor or average, it is optimal to search far away on the technology landscape; but as the firm succeeds in finding technological improvements it is optimal to confine search to a local region of the landscape. We obtain the result that there are diminishing returns to search without having to make the assumption that the firm's repeated draws from the search space are independent and identically distributed.